Roadmap for Monomer Conversion and Chain Length-Dependent Termination Reactivity Algorithms in Kinetic Monte Carlo Modeling of Bulk Radical Polymerization

Abstract

Radical polymerization is prone to diffusional limitations on termination, leading to a rate acceleration by the gel-effect and molecular changes, with strong increases in average chain length in free radical polymerization (FRP) and improvement of the end-group functionality in reversible deactivation radical polymerization. What complicates the correct implementation of the termination rates in kinetic modeling studies is (i) the chain length and monomer conversion dependence of the individual (apparent) termination rate coefficients (k t,app,ij values; i,j: chain length) and (ii) the wide variations in macroradical chain length distribution (CLD) types and shapes along the polymerization and upon altering the reaction conditions, including variations in CLD modality and broadness. In this work, we compare four major kinetic Monte Carlo modeling algorithms to sample termination reaction events in bulk radical polymerization, using literature k t,app,ij values. We present a roadmap allowing one to select the most suited algorithm depending on the radical polymerization technique and reaction conditions, therefore opening the pathway to more correct representations of chain length and monomer conversion dependencies in radical polymerization. Case studies are related to bulk nitroxide-mediated polymerization, FRP, and pulsed laser polymerization, following an increasing complexity in the active macroradical CLD type and shape.

Conformational Variations for Surface-Initiated Reversible Deactivation Radical Polymerization: From Flat to Curved Nanoparticle Surfaces

“…Regarding termination reactions that are purely occurring in the solution, the composite k t model from Johnston-Hall and Monteiro 85 is utilized to account for the dependency of the apparent termination rate coefficients on polymer mass fraction and chain length. We use the population-weighted method 87 to update the apparent average termination rate coefficient that codefines the global sampling of the termination reaction channel in the solution and corrects for diffusional limitations. Consistent with the work of De Keer et al 73 no additional factor 2 is included to reflect the likelihood that the two radicals involved have a different chain length.…”

“…This relates to the verification of (i) mobility variations of chains from the solution via segmental diffusion to the active center of the envisaged anchored species and (ii) availability of space to include the next chemical moiety. For termination rates in the solution, diffusional limitations − are also considered by taking into account chain length and polymer mass fraction variations. e For simplicity, the nominal values of the elementary rate coefficients for chain initiation and propagation reactions on the surface ( k i ,surf and k p,surf ) as well as termination reactions between surface-tethered and solution-free macrospecies ( k tc,sol‑surf and k td,sol‑surf ) adopt the same values as those in the solution near the surface, based on the work of Zhu and co-workers. ,,, All rate coefficients have also been reported in our previous work with key input from Zhong and Matyjaszewski …”

“…This relates to the verification of (i) mobility variations of chains from the solution via segmental diffusion to the active center of the envisaged anchored species and (ii) availability of space to include the next chemical moiety. For termination rates in the solution, diffusional limitations − are also considered by taking into account chain length and polymer mass fraction variations.…”

Exploiting (Multicomponent) Semibatch and Jacket Temperature Procedures to Safely Tune Molecular Properties for Solution Free Radical Polymerization of n‐Butyl Acrylate

“…We apply the so‐called sampling method, which was demonstrated as promising in previous work, with an update of < k t,app > every time a termination event has taken place. [ 61 ] This means that we start the simulation with the k t,11,app value (so the highest “intrinsic” value) and every time the SSA selects termination from the complete list of reaction channels (or equivalently types), we select two chain lengths i and j from the previous termination event. These chain lengths are then used to approximate < k t,app > at the polymer mass fraction established at that moment, which is subsequently utilized in the sampling of reaction types.…”

In Silico Screening To Achieve Fast Lab-Scale Nitroxide-Mediated Polymerization of n-Butyl Acrylate with Maximal Control over Macromolecular Properties

“…For termination, in line with previous work on FRP, the composite k t model with its parameters tuned in specialized kinetic studies is utilized. , This physical model delivers apparent termination rate coefficients that account for polymer mass fraction and chain length dependencies (Table S3 of the Supporting Information). The implementation of the composite k t model into SSA is performed through the sampling method, which updates the average termination rate coefficient < k t,app > (over the whole radical population) every time a termination event is selected, using two randomly selected chain lengths i and j from the radical population.…”